Fosterage

Fosterage was the act of raising an offspring that was not one's own as if it was one's own, but unlike adoption, the actual parents were generally acknowledged as the rightful parents. The term surrogate was applied in post-partum (beyond being a surrogate parent) or towards a young adult (where one may seek out or require a father figure).

In Klingon, a similar term was soh-chim, the formalized arrangement that assigned one to be responsible for a child in the event of his parent's death. In an alternate timeline, Worf asked Deanna Troi to act as the soh-chim to Alexander, which he described compared to being his surrogate mother. (TNG: "Parallels")